Simplified conditions and configurations for phase-contrast imaging with hard x-rays

ABSTRACT

A method of obtaining an image of a boundary of an object, the boundary representing a refractive index variation, the method including irradiating the boundary with penetrating radiation having high lateral spatial coherence and a propagation component transverse to the refraction index variation, and receiving at least a portion of the radiation on an image plane so as to form the image, the radiation having been refracted by the boundary such that the boundary is represented on the image by a corresponding intensity variation. Additionally, the method may also include processing the image to resolve weaker variations.

CROSS-REFERENCES TO RELATED APPLICATIONS Related Applications

This is a continuation of Ser. No. 08/930,049 filed Sep.26, 1997, nowU.S. Pat. No. 6,018,564, and having an international filing date of Mar.28, 1996.

BACKGROUND OF THE INVENTION

This invention relates generally to the observation of a structuralfeature of an object utilizing penetrating radiation such as x-rays.More particularly, but not exclusively, the invention relates to x-rayphase-contrast recordal, e.g. imaging, of internal boundary features.

The present applicant's international patent publication WO95/05725(PCT/AU94/00480) and provisional patent application PN5811/95 disclosevarious configurations and conditions suitable for differentialphase-contrast imaging using hard x-rays. Other disclosures are to befound in Soviet patent 1402871 and in U.S. Pat. No. 5,319,694. It isdesired that relatively simpler conditions and configurations moreclosely related, at least in some embodiments, to traditional methods ofabsorption-contrast radiography, may be utilised for differentialphase-contrast imaging with hard x-rays.

In accordance with the present invention there is provided a method ofobtaining an image of a boundary of an object, said boundaryrepresenting a refractive index variation, said method including:

irradiating said boundary with penetrating radiation having high lateralspatial coherence and a propagation component transverse to saidrefraction index variation; and

receiving at least a portion of said radiation on an image plane so asto form said image, said radiation having been refracted by saidboundary such that said boundary is represented on said image by acorresponding intensity variation.

The present invention further provides an apparatus for obtaining animage of a boundary of an object, said boundary representing arefractive index variation, said apparatus including:

a source for irradiating said boundary with penetrating radiation havinghigh lateral spatial coherence and a propagation component transverse tosaid refraction index variation; and

a detector for receiving at least a portion of said radiation so as toform said image, said radiation having been refracted by said boundarysuch that said boundary is represented on said image by a correspondingintensity variation.

The present invention also provides a method of deriving aphase-contrast record of an internal boundary having a sharp refractiveindex variation or defined by a thickness variation, comprising:

irradiating the boundary with penetrating radiation having a propagationdirection such that there is a significant component of the propagationvector transverse to the direction of said refractive index variation orin the direction of said thickness variation, and further having alateral spatial coherence sufficiently high for the variation inrefractive index or thickness to cause a detectable change in the localdirection of propagation of the radiation wavefront at the boundary; and

detecting and recording at least a portion of said radiation after ithas traversed said boundary in a manner whereby an effect of said changein the local direction of propagation is observable and thereby recordedas a local diminution or rapid variation of intensity of the radiationwhich thereby substantially images the boundary.

The present invention further provides an apparatus for deriving aphase-contrast record of an internal boundary having a sharp refractiveindex variation or defined by a thickness variation, comprising:

means to irradiate the boundary with x-ray radiation having apropagation direction such that there is a significant component of thepropagation vector transverse to the direction of said refractive indexvariation or in the direction of said thickness variation, and furtherhaving a lateral spatial coherence sufficiently high for the variationin refractive index or thickness to cause a detectable change in thelocal direction of propagation of the radiation wavefront at theboundary; and

means to detect and record at least a portion of said radiation after ithas traversed said boundary in a manner whereby an effect of said changein the local direction of propagation is observable and thereby recordedas a local diminution or rapid variation of intensity of the radiationwhich thereby substantially images the boundary.

The present invention also provides a method of obtaining an image of aboundary of an object, said boundary representing a refractive indexvariation, said method including:

irradiating said boundary with penetrating radiation having high lateralspatial coherence and a propagation component transverse to saidrefraction index variation; and

receiving at least a portion of said radiation on an image plane so asto form said image, said radiation having been Fresnel diffracted bysaid boundary such that said boundary is represented on said image by acorresponding intensity variation.

The present invention further provides an apparatus for obtaining animage of a boundary of an object, said boundary representing arefractive index variation, said apparatus including:

a source for irradiating said boundary with penetrating radiation havinghigh lateral spatial coherence and a propagation component transverse tosaid refraction index variation; and

a detector for receiving at least a portion of said radiation so as toform said image, said radiation having been Fresnel diffracted by saidboundary such that said boundary is represented on said image by acorresponding intensity variation.

The present invention also provides a method of determining the phase ofan image, including processing phase-contrast image data of said image.

The intensity effect of a change in the local direction of propagationis preferably observable in an image comprising the record. The recordand therefore the image may be photographic or electronic. The term“image” may thus refer, for example, to an observable effect in a set ofintensity data, for example a table or other stored record of intensityvalues: the term is not confined to a visual context. The recordingmedium may comprise a two-dimensional pixilated detector, e.g. anelectronic detector such as a charge-coupled device (CCD) array.

The irradiating means preferably includes a source of x-rays of diameter20 micron or less, where diameter refers to the full width of intensitydistribution of the source at half maximum intensity. The apparatus mayadvantageously further include a suitable stage or holder for samplescontaining the internal boundary being imaged.

The penetrating radiation, e.g. x-ray radiation, may be polychromaticand is preferably in the hard x-ray range, i.e. in the range 1 keV to 1MeV.

The separation of the boundary and the detecting means is preferablyselected to enhance the resolution of the image. For example, it hasbeen observed that a sharper image, i.e. one with better contrast, isachieved by increasing separation. For instance contrast is improved atleast for a separation of about 1 m relative to a separation of 0.4 m.This may partly be because background noise is diminished withincreasing separation but the intensity variation effect arising fromthe change in the local direction of propagation is substantiallypreserved.

The term “lateral spatial coherence” herein refers to the correlation ofthe complex amplitudes of waves between different points transverse tothe direction of propagation of the waves. Lateral spatial coherence issaid to occur when each point on a wavefront has a direction ofpropagation which does not change over time. In practice, high lateralspatial coherence may, for example, be achieved by using a source ofsmall effective size or by observing the beam at a large distance fromthe source. For example, for 20 keV x-rays a source size of 20 μmdiameter or less would typically be appropriate. The smaller the sourcesize the better for the purposes of this invention, provided total fluxfrom the source is sufficient. Lateral spatial coherence may need to bepreserved by careful selection of the x-ray window of the source, e.g.such that it is of highly uniform thickness and homogeneity.

SUMMARY OF THE INVENTION

Preferred embodiments of the present invention are hereinafterdescribed, by way of example only, with reference to the accompanyingFigures, in which:

FIG. 1 is a diagram, presented in three parts for purposes ofillustration, showing a circular cross-section object being irradiatedby a parallel beam;

FIG. 2 is a diagram of a circular cross-section object being irradiatedby a polychromatic beam and the intensity of the phase-contrast imageproduced;

FIG. 3 is a diagram of an x-ray optics configuration according to anembodiment of the invention; and

FIGS. 4 and 5 are x-ray images of various boundaries derived inaccordance with the invention, as subsequently detailed herein.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

It is first now proposed to outline the mathematical basis of thepresent invention.

Variations in thickness and x-ray refractive index, n(λ)=1−δ(λ)−iβ(λ),of a sample will invariably lead to a change in the shape of an x-raywavefront on passing through the sample. The real component 1−δ(λ) of nrelates to the degree of refraction and the imaginary component −β(λ)relates to the degree of absorption. More specifically, for a singleelement substance $\begin{matrix}{{\delta (\lambda)} = {\frac{r_{o}\lambda^{2}}{2\pi}N_{o}f_{R}}} & (1) \\{{\beta (\lambda)} = {\frac{\lambda}{4\pi}{\mu (\lambda)}}} & (2)\end{matrix}$

where μ(λ) is the linear absorption coefficient, r_(o) is the classicalradius of an electron, N_(o) is the number of atoms per unit volume andf_(R) is the real part of the atomic scattering factor at zeroscattering angle. The coefficient δ is proportional to λ² and β isproportional to λ⁴ and also λ is proportional to 1/energy of the x-rayphoton emitted from the source.

The magnitude of the wavefront distortions is related to the gradient ofthe phase variations transverse to the direction of propagation of thewavefront. In the geometrical optics approximation, the phasedifference, φ, for a ray path through an object is proportional to theintegral of the decrement of the real part of the refractive index, δ,along that ray path. For the coordinate system illustrated in FIG. 1this can be expressed generally as $\begin{matrix}{{\varphi \left( {x,z} \right)} = {k{\int_{o}^{z}{\left\{ {{n\left( {x,z^{\prime}} \right)} - 1} \right\} {z^{\prime}}}}}} & (3)\end{matrix}$

where k is equal to 2π/λ. The angular deviation Δα of the localscattered wavevector from that of the local incident wavevector isproportional to the gradient of the phase difference in the directionperpendicular to the local incident wavevector. The word “local” refersto a point (x,y,z) on the wavefront. Mathematically the local scatteredwavevector can be written for the coordinate system illustrated in FIG.1 as $\begin{matrix}{{s\left( {x,y,z} \right)} \simeq \left( {\frac{\partial\varphi}{\partial x},\frac{\partial\varphi}{\partial y},k} \right)} & (4)\end{matrix}$

where s(x,y,z) is the normal to the wavefront at point (x,y,z) and theabove relationship is valid in the paraxial approximation when(∂φ/∂x)²+(∂φ/∂y)²<<k². The angular deviation Δα can be expressed as$\begin{matrix}{{{\Delta\alpha} \simeq {\frac{1}{k}\frac{\partial{\varphi \left( {x,z} \right)}}{\partial x}}} = {\int_{o}^{z}{\left\{ {\frac{\partial{n\left( {x,z^{\prime}} \right)}}{\partial x} - 1} \right\} {{z^{\prime}}.}}}} & (5)\end{matrix}$

The angular deviation Δα is therefore dependent on a refractive indexvariation perpendicular to a propagation wavevector, and the amount ofdeviation depends on the length over which the variation occurs in thedirection of the wavevector, e.g. the thickness of a sample.

To illustrate the nature of the effect, consider the case of a sphericalobject, Ω, of refractive index n_(M) embedded in a medium of refractiveindex n_(o)=1, as illustrated in FIGS. 1 and 2.

The x-ray optical path length differences through the sample relative tothrough a vacuum lead to a phase difference φ(x) and hence to a phasegradient ∂φ/∂x in the direction (FIG. 1) transverse to the localdirection of propagation. The phase difference between ray 1 whichpasses through the object Ωparallel to the z-axis at constant distancefrom it and the reference ray 0 is: $\begin{matrix}{{{\varphi \left( {x,y} \right)} = {{\frac{2\pi}{\lambda}{\int_{- {z{({x,y})}}}^{o}{{\delta (\lambda)}{t}}}} = {\frac{2\pi}{\lambda}{\delta (\lambda)}{x\left( {x,y} \right)}}}},} & (6)\end{matrix}$

where z(x,y) is the length of the intersection of ray 1 with Ω and

z(x,y)=2{square root over (R²−x²+L −y²+L )},  (7)

and R is the radius of Ω and δ is the decrement of refractive indexcoefficient. Mathematically, for a circular sectioned object in the x-zplane, the expression for ∂φ/∂x and the angular deviation ha between anincident ray and the corresponding refractive ray for a given x is:$\begin{matrix}\begin{matrix}{{\Delta\alpha} = {\frac{1}{k}{s\left( {x,y,z} \right)}}} \\{= {\frac{\lambda}{2\pi}\frac{\partial\varphi}{\partial x}}} \\{= {{- 2}{{{\delta (\lambda)}\left\lbrack \frac{x}{\sqrt{R^{2} - x^{2}}} \right\rbrack}.}}}\end{matrix} & (8)\end{matrix}$

In equation (8), δ(λ) is slowly varying and it can readily be seen thatthe phase gradient diverges at x=±R, where the rays can deviate by verylarge angles from the optic axis. In these limits, the angulardeviations of the scattered beams can be very large and lead to anobservable loss in intensity I in the corresponding forward direction,the position of which is independent of wavelength, as shown in FIG. 2for a polychromatic beam B. The decrement of refractive indexcoefficient, δ, is typically of order 10⁻⁵ to 10⁻⁶ for light elementsand hard x-rays but nevertheless the deviation angle Δα may be quitelarge when x is close to ±R, i.e. at the boundary of the sample or at aninternal boundary feature.

The nature of the contrast obtained under different conditions of sourcesize, object-source distance and object-image distance, and also thespectral distribution of the source need to be considered. A furtherconsideration affecting contrast is the degree of modification of thewavefront introduced by the object.

For the plane-wave case, to help understand the role of these factors oncontrast in image formation, we can to a first approximation use theformula derived by Cowley (J. M. Cowley, “Diffraction Physics”, 2nd Ed.,p.60, North Holland, 1981) for the Fresnel diffraction contrast from aphase object. According to this formal, for a one-dimensional phaseobject producing a phase change, φ(x), under plane-wave illuminationwith wavelength λ, the intensity distribution at a distance R₂ from theobject is given by $\begin{matrix}{{I(x)} = {1 + {\frac{R_{2}\lambda}{2\pi}{\varphi^{''}(x)}}}} & (9)\end{matrix}$

which is valid to first order in the quantity (R₂λ/2π)φ″(x), assumedsmall. From this apparently simple formula, one can draw somesignificant conclusions, namely:

i) the contrast varies directly with R₂,

ii) the structure of the image is λ-independent. Only the contrast isaffected. For a polychromatic source one would simply replace λ in theformula by a spectrally weighted sum.

To get some feeling for the range of validity of the above formula forthe present x-ray case, let us suppose there is an object feature forwhich the phase transmitted by the object varies by 1 radian over alateral distance of 10 microns. Then φ″˜10¹⁰m⁻², and for λ˜1 Å, R₂˜1m,we see that (R₂λ/2π)′″(x)≦1. Thus the formula should be valid even forsmall phase objects or reasonably rapid variations in phase. However,for very sharp edges or changes of slope, such as are often used incalculations of artificial test objects (e.g. fibres), φ″ may become toolarge (even infinite), so the formula breaks down. But even in thesecases the general form of the image (a black/white line from a sharpstep object) is reproduced but not the subsidiary fringes typical ofdiffraction from such discontinuities. On the other hand, and probablyof more practical significance, we see that for smaller φ″(x), i.e.larger features with less rapid lateral variation, the contrast will below, and may well limit the practical visibility.

A more exact mathematical treatment of this type of imaging withplane-waves has recently been carried out in terms of Fresneldiffraction (P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay and M.Schlenker, J. Phys. D.: Appld. Phys., 1996 29, 133-46; J. P. Guigay,Optik, 1977 49, 121-5). Their treatment gives the same equation aspresented above to first order. However the more accurate treatmentleads to the conclusion that the maximum contrast for a spatialfrequency u occurs when 2λR₂u²=1, at least for the normal range ofconditions expected in phase-contrast radiography. The spatial frequencyu relates to the structure of the object being imaged, where u equals1/A where A is the spatial period of a Fourier component of the imagedobject.

These treatments all refer to illumination with an ideal plane-wave. Anydivergence in the beam will blur the image by an amount proportional toR₂ (in this respect behaving in the same way as in conventionalradiography). The above authors (Cloetens et al.) then show that theoverall optimum R₂, taking into account both contrast and resolution isgiven by

R ₂≦2λ/α ²  (10)

where α=s/R₁ is the angle subtended by the source at the object andrelates to the (almost) plane-wave case. It should be noted thatCloetens et al. specifically prescribe the need for a highlymonochromatic source of x-rays and consider only the plane-wave case incontradistinction to the preferred embodiments described herein.

As pointed out, the treatments above relate specifically to theplane-wave case whereas we are principally concerned with thespherical-wave case which more closely relates to conventionradiography. To help understand the spatial-wave case, we now considerthe relationship between the two which can be usefully established via asimple analysis of the Fresnel-Kirchhoff expression for imaging anobject with a point source at a distance R₁ from the object (thespherical-wave case). This shows that there is a simple relationship forthe spherical-wave case involving terms of the plane-wave case but witha modified object to image distance R′, such that $\begin{matrix}{\frac{1}{R^{\prime}} = {\frac{1}{R_{1}} + \frac{1}{R_{2}}}} & (11)\end{matrix}$

and with the image magnified by (R₁+R₂)/R₁. From simple geometricalarguments, based on ray optics, it appears that loss of contrast orresolution due to source size will not be a problem in thespherical-wave case as both the image and the source size are magnified,the latter by R₂/R₁ which asymptote to the same factor for large R₂. Thefactor affecting contrast for the spherical-wave case is that (for therange of energies and spatial resolutions relevant for radiography)2λR₂(1+R₂/R₁)u² should be large (but is typically less than 1). Thisexpression may be large because R₂ is large, or λ large or the spatialfrequency, u, is large. As an illustration, for practical radiographicpurposes the following values might serve as being indicative λ=0.2 Å;u≦2×10⁵ (corresponding to a spatial period of 20 micron or more) so thatR₂≈2.5 m (assuming R₂/R₁=3, say) would give maximum contrast for thehighest spatial frequency. Larger values of R₂ would be appropriate formaximum contrast of lower spatial frequencies.

It may be noted that the function φ″ will tend to enhance the edges andboundaries of a phase object in an image. If there is also an absorptivecomponent of the object it will, at least to first order, add directlyto the image contrast (e.g. see Equation 7 in Guigay, 1977). The presenttechnique could complement and enhance the usual radiological image, aswell as yielding new information. It may also be noted that propertreatment of the contrast in an image involving differentialphase-contrast (involving the Laplacian of φ) requires numericalprocessing of the image via, for example, solution of the transport ofintensity equations (see T. E. Gureyev, A. Roberts and K. Nugent,Journal of Optical Society of America, Vol. A12, pp.1932 and pp.1942,1995 incorporated herein by reference) in order to retrieve the phase,φ(x).

We turn now to practical arrangements for applying the concept arisingfrom these determinations. In a first embodiment (FIG. 3), there is asource S of high spatial coherence and an x-ray imaging detector D, forexample film, photostimulable phosphor plates (e.g. Fuji Image Plates),or a two-dimensional electronic detector, for recording images forprocessing P utilizing the formulae and techniques discussed above.Regions of sharp refractive index variation transverse to the directionof propagation, or thickness variation in the direction of propagation,can lead to a significant change in the local direction of propagationof the wavefront passing through those regions. Thus a sphericalwavefront W1 emanating from the point source S, which may be consideredto be unfocused, becomes distorted to W2 on passing through the objectO. This distorted, unfocused wavefront falls upon and is detected byx-ray detector D. By recording the intensity of the wavefront at asufficient distance from the sample, intensity variations due to sharprefractive index and thickness variations in the sample may be detectedand their location recorded in an image. This corresponds to a form ofdifferential phase-contrast imaging. The location of the imagingdetector is chosen such that the spatial resolution of the detector issufficient to resolve the intensity differences arising from the severedistortions of the wavefront and to optimise contrast, as describedabove, subject to practical considerations.

Typically, the sharp gradients in refractive index or thickness will beimaged as sharp losses or rapid variation in intensity at correspondingpoints in the image. This feature of intensity loss or rapid variationat a given point in the image is essentially independent of wavelengthand can therefore lead to very sharp contrast variations in the imageeven when a polychromatic source is used.

This configuration has the feature that for a circular sourcedistribution, the spatial resolution in the image is the same for bothdirections and is essentially determined by the source size. It also hasthe advantage that considerable magnification of the image is possibleand so recording media such as Fuji Image Plates may be used which havemany desirable properties such as wide dynamic range and highsensitivity but not high spatial resolution.

In addition to the source and detector involved in this configuration, ahigh resolution angular analyzer may be inserted between the sample andthe detector. The high resolution angular analyser might for example bea suitably curved crystal in Laue geometry with curvature chosen forsome appropriate characteristic wavelength of the source. This variationin the method is aimed at resolving weaker variations in refractiveindex and thickness of the sample than are observable with the firstdescribed configuration.

It may be noted that a very substantial magnification of the image ispossible so that very high spatial resolution in the image may beachieved even with much lower spatial resolution detectors such as FujiImage Plates. Also it may be noted that since the method of imageformation is essentially independent of x-ray energy, the sources can beoperated at high tube voltage and so lead to lower absorbed dose to thesample, which is important in clinical applications.

Some examples of phase-contrast images recorded using the aforementionedtechnique are illustrated in FIGS. 4 and 5. FIG. 4 shows an image of theedge of a 10 μm plastic film which is the same as that used in Davis,Gao, Gureyev, Stevenson and Wilkins (Phys. Rev. Letters, 1995, Vol. 74,p. 3173) and corresponds to a pure phase object. FIG. 5 shows images ofan air bubble and glass fibres in a polymer matrix based on a similarsample to that reported in Davis, Gao, Gureyev, Stevenson and Wilkins(Nature Vol. 373 pp. 595-8, 1995) and corresponds to an almost purephase object. In each case clear additional contrast can be seen overthat expected for a normal absorption-contrast image. In particular, inFIG. 4 the edge of the film is clearly visible as a black/white contrastfeature as also are the edges of the bubbles and the fibres. The sourceused was a nominal 10 μm diameter microfocus source (Kevex Model PXS)with Cu anode operated at 40 kV. For FIG. 4 the source to sample andsample to film distances were both 700 mm while for FIG. 5 thecorresponding distances were 120 mm and 1000 mm, respectively. It shouldbe noted that contrast in the present instances is visible almostentirely due to the high spatial coherence of the source. The contrastis primarily an intensity loss contrast and in that sense resemblesnormal absorption but is different in that it represents an intensityloss due to refractive scattering (or Fresnel diffraction) at the objectboundaries as shown by equation (8). A normal fine focus source ofdiameter 0.1 mm would have a projected size of approximately the lengthof the 0.1 mm scale bar shown on the photographs and so largely smearout this contrast.

To provide a comparison of phase-contrast imaging as described hereinand standard absorption imaging, the table below sets out the absorptionthickness t₂ of a carbon sample required to achieve 65% absorption andthe phase thickness t_(p) of the sample required to achieve a phasechange in φ of 2π, for different source energies E.

TABLE 1 E keV λ(Å) t_(a)(μm) t_(p)(μm) 50 0.25 435000 133 12 1 5000 301.2 10 4 3 0.25 50 1.3 1.2

The results in the table illustrate how phase-contrast imaging can beused to image very small objects with high energy sources.

Advantageously, the beam path between sample and detector may involveevacuated tubes with x-ray transparent windows or similar means toreduce the effects of air scattering making sure that their opticalquality is such that they do not have a detrimental effect on thecoherence of the x-ray beam.

The present method should be especially well suited to imaging of suchfeatures as cracks, voids and delamination effects in various types ofmaterials, since these features involve maximum differences in x-rayrefractive index and the spatial variation can be extremely sharp. Togive observable contrast, the source is preferably of a very smalleffective size, say less than of order 20 μm, and the detector ispreferably a high resolution imaging detector such as x-ray film or atwo-dimensional electronic detector, e.g. a CCD array. The method mayalso prove useful in significantly enhancing the contrast of importantfeatures in clinical radiography.

The present application outlines some simplified conditions andconfigurations for differential phase-contrast imaging using penetratingradiation such as hard x-rays, which are particularly aimed at clinicaland industrial applications. These new approaches are more closelyrelated to traditional methods used for absorption-contrast radiographyand should be easier to implement than our earlier described methods ofthe aforementioned WO95/05725 and PN5811/95, especially for large areasof irradiation. They should also have considerably shorter exposuretimes for a given source power than the earlier monochromatic methodssince they may use a very wide spectrum from the source.

Throughout this specification, unless the context requires otherwise,the word “comprise”, or variations such as “comprises” or “comprising”,will be understood to imply the inclusion of a stated integer or groupof integers but not the exclusion of any other integer or group ofintegers.

What is claimed is:
 1. A method of obtaining an image of a boundary ofan object, said boundary representing a refractive index variation, saidmethod comprising: irradiating said boundary with a propagated wavefrontof x-rays having high lateral spatial coherence and a propagationcomponent transverse to said refractive index variation; detectingintensity of at least a portion of said wavefront of said x-rays passingthrough said boundary so as to form said image, said x-rays having beenrefracted by said boundary such that said boundary is represented onsaid image by a corresponding variation in the detected intensity ofsaid wavefront in said image; and processing said image so as to derivefrom the image said corresponding variation in the detected intensity ofsaid wavefront in said image and so identify the representation of theboundary.
 2. A method as claimed in claim 1, wherein said x-rays arepolychromatic.
 3. A method as claimed in claim 1, wherein said step ofirradiating said boundary comprises irradiating said boundary with anunfocused propagated wavefront of x-rays, and wherein said step ofdetecting intensity comprises detecting intensity of at least a portionof said wavefront of said x-rays passing through said boundary so as toform said image without focusing said wavefront after it passes throughsaid boundary.
 4. A method as claimed in claim 1, including separatingthe boundary and the position of detecting said intensity of at least aportion of said wavefront by a distance sufficient to enhance thecontrast of said variation in the detected intensity of said wavefront.5. A method as claimed in claim 4, wherein said distance is greater thanor equal to 0.3 m.
 6. A method as claimed in claim 5, wherein saiddistance is greater than or equal to 0.7 m.
 7. A method as claimed inclaim 1, wherein said x-rays have an energy in the range 1 keV to 1 MeV.8. A method as claimed in claim 1, including generating said x-rays witha source less than or equal to 20 μm in diameter.
 9. A method as claimedin claim 1, wherein said variation in the detected intensity of saidwavefront is sharp and localized.
 10. An apparatus for obtaining animage of a boundary of an object, said boundary representing arefractive index variation, said apparatus comprising: a source forirradiating said boundary with a propagated wavefront of x-rays havinghigh lateral spatial coherence and a propagation component transverse tosaid refractive index variation; a detector for detecting intensity ofat least a portion of said wavefront of said x-rays so as to form saidimage, said x-rays having been refracted by said boundary such that saidboundary is represented on said image by a corresponding variation inthe detected intensity of said wavefront in said image; and means forprocessing said image so as to derive from the image said correspondingvariation in the detected intensity of said wavefront in said image andso identify the representation of the boundary.
 11. An apparatus asclaimed in claim 10, further including holder means to hold an objectcontaining said boundary and so locate the boundary at a predeterminedposition, whereby a separation distance between said boundary and saiddetector may be set to enhance the contrast of said variation in thedetected intensity of said wavefront.
 12. An apparatus as claimed inclaim 11, wherein said detector and said holder means are disposed sothat said distance is greater than or equal to 0.3 m.
 13. An apparatusas claimed in claim 11, wherein said detector and said holder means aredisposed so that said distance is greater than or equal to 0.7 m.
 14. Anapparatus as claimed in claim 10, wherein said source generates x-rayswith energy in the range 1 keV to 1 MeV.
 15. An apparatus as claimed inclaim 10, wherein said source has a diameter less than or equal to 20μm.
 16. An apparatus as claimed in claim 10, wherein said x-rays arepolychromatic.
 17. An apparatus as claimed in claim 10, wherein saidvariation in the detected intensity of said wavefront is sharp andlocalized.
 18. A method of deriving a phase-contrast record of aninternal boundary representing a sharp refractive index variationcomprising: irradiating the boundary with a propagated wavefront ofx-rays having a propagation direction such that there is a significantcomponent of the propagation vector transverse to the direction of saidrefractive index variation, and further having a lateral spatialcoherence sufficiently high for the variation in refractive index tocause a detectable change in the local direction of propagation of thewavefront of x-rays at the boundary; detecting and recording intensityof at least a portion of said wavefront of x-rays after it has traversedsaid boundary in a manner whereby an effect of said change in the localdirection of propagation is observable to form a record of a localdiminution or rapid variation of intensity of the x-rays which therebysubstantially detects the boundary; and processing said record so as toderive from the record said corresponding variation in the detectedintensity of said wavefront in said record and so identify therepresentation of the boundary.
 19. A method as claimed in claim 18,wherein said x-rays are polychromatic.
 20. A method as claimed in claim18, wherein said step of irradiating said boundary comprises irradiatingsaid boundary with an unfocused propagated wavefront of x-rays, andwherein said step of detecting intensity comprises detecting intensityof at least a portion of said wavefront of said x-rays passing throughsaid boundary so as to form said record without focusing said wavefrontafter it passes through said boundary.
 21. A method as claimed in claim18, including separating said boundary and the position of detectingsaid portion of said x-rays by a distance which enhances the contrastand/or resolution of the part of an image comprising the record of saidlocal diminution or rapid variation of wavefront intensity.
 22. A methodas claimed in claim 18, wherein said x-rays have an energy in the range1 keV to 1 MeV.
 23. A method as claimed in claim 18, wherein said stepof irradiating comprises irradiating said boundary with an x-ray sourcehaving a diameter less than or equal to 20 μm.
 24. A method as claimedin claim 21, wherein said distance is greater than or equal to 0.3 m.25. A method as claimed in claim 21, wherein said distance is greaterthan or equal to 0.7 m.
 26. An apparatus for deriving a phase-contrastrecord of an internal boundary representing a sharp refractive indexvariation, comprising: means to irradiate the boundary with a propagatedwavefront of x-rays having a propagation direction such that there is asignificant component of the propagation vector transverse to thedirection of said refractive index variation, and further having alateral spatial coherence sufficiently high for the variation inrefractive index to cause a detectable change in the local direction ofpropagation of the wavefront of x-rays at the boundary; and means fordetecting and recording intensity of at least a portion of saidwavefront of x-rays after it has traversed said boundary in a manner,whereby an effect of said change in the local direction of propagationis observable to form a record of a local diminution or rapid variationof intensity of the wavefront of x-rays which thereby substantiallydetects the boundary; and means for processing said record so as toderive from the record said corresponding variation in the detectedintensity of said wavefront in said record and so identify therepresentation of the boundary.
 27. An apparatus as claimed in claim 26,wherein said x-rays are polychromatic.
 28. An apparatus as claimed inclaim 26, wherein said x-rays have an energy in the range 1 keV to 1MeV.
 29. An apparatus as claimed in claim 26, wherein said means toirradiate is a source less than or equal to 20 μm in diameter.
 30. Anapparatus as claimed in claim 26, further including holder means to holdan object containing said boundary and so locate the boundary at apredetermined position, whereby the separation of said boundary and theposition of detecting said portion of said wavefront of x-rays may beset at a distance which enhances the contrast and/or resolution for partof an image comprising the record of said local diminution or rapidwavefront variation of intensity.
 31. An apparatus as claimed in claim30, wherein said detection means and said holder means are disposed sothat said distance is greater than or equal to 0.3 m.
 32. An apparatusas claimed in claim 30, wherein said detection means and said holdermeans are disposed so that said distance is greater than or equal to 0.7m.
 33. A method of obtaining an image of a boundary of an object, saidboundary representing a refractive index variation, said methodcomprising: irradiating said boundary with a propagated wavefront ofx-rays having high lateral spatial coherence and a propagation componenttransverse to said refractive index variation; detecting intensity of atleast a portion of said wavefront of said x-rays so as to form saidimage, said x-rays having been Fresnel diffracted by said boundary suchthat said boundary is represented on said image by a correspondingvariation in the detected intensity of said wavefront in said image; andprocessing said image so as to derive from the image said correspondingvariation in the detected intensity of said wavefront in said image andso identify the representation of the boundary.
 34. A method as claimedin claim 33, wherein said step of irradiating said boundary comprisesirradiating said boundary with an unfocused propagated wavefront ofx-rays, and wherein said step of detecting intensity comprises detectingintensity of at least a portion of said wavefront of said x-rays passingthrough said boundary so as to form said image without focusing saidwavefront after it passes through said boundary.
 35. An apparatus forobtaining an image of a boundary of a object, said boundary representinga refractive index variation, said apparatus comprising: a source forirradiating said boundary with a wavefront of x-rays having high lateralspatial coherence and a propagation component transverse to saidrefractive index variation; and a detector for receiving at least aportion of said wavefront of said x-rays passing through said boundaryso as to form said image, said x-rays having been Fresnel diffracted bysaid boundary such that said boundary is represented on said image by acorresponding variation in the detected intensity of said wavefront insaid image; and means for processing said image so as to derive from theimage said corresponding variation in the detected intensity of saidwavefront in said image and so identify the representation of theboundary.